3.1 Description

The ICU Admission dataset contains observations of patients that were admitted to an adult intensive care unit (ICU). The response variable of this dataset is Status of patients after admission, that is, whether they lived or died after admission to ICU. A description of the variables is available below.

Number of cases: 200
Variable Names:

1. ID: ID number of the patient
2. STA: Vital status (0 = Lived, 1 = Died)
3. AGE: Patient’s age in years
4. SEX: Patient’s sex (0 = Male, 1 = Female)
5. RACE: Patient’s race (1 = White, 2 = Black, 3 = Other)
6. SER: Service at ICU admission (0 = Medical, 1 = Surgical)
7. CAN: Is cancer part of the present problem? (0 = No, 1 = Yes)
8. CRN: History of chronic renal failure (0 = No, 1 = Yes)
9. INF: Infection probable at ICU admission (0 = No, 1 = Yes)
10. CPR: CPR prior to ICU admission (0 = No, 1 = Yes)
11. SYS: Systolic blood pressure at ICU admission (in mm Hg)
12. HRA: Heart rate at ICU admission (beats/min)
13. PRE: Previous admission to an ICU within 6 months (0 = No, 1 = Yes)
14. TYP: Type of admission (0 = Elective, 1 = Emergency)
15. FRA: Long bone, multiple, neck, single area, or hip fracture (0 = No, 1 = Yes)
16. PO2: PO2 from initial blood gases (0 = >60, 1 = ²60)
17. PH: PH from initial blood gases (0 = ³7.25, 1 <7.25)
18. PCO: PCO2 from initial blood gases (0 = ²45, 1 = >45)
19. BIC: Bicarbonate from initial blood gases (0 = ³18, 1 = <18)
20. CRE: Creatinine from initial blood gases (0 = ²2.0, 1 = >2.0)
21. LOC: Level of consciousness at admission (0 = no coma or stupor, 1= deep stupor, 2 = coma)

4.1 Structure of the ICU dataset

> str(ICU)

'data.frame':   200 obs. of  21 variables:
 $ ID           : int  8 12 14 28 32 38 40 41 42 50 ...
 $ Status       : int  0 0 0 0 0 0 0 0 0 0 ...
 $ Age          : int  27 59 77 54 87 69 63 30 35 70 ...
 $ Sex          : int  1 0 0 0 1 0 0 1 0 1 ...
 $ Race         : int  1 1 1 1 1 1 1 1 2 1 ...
 $ Service      : int  0 0 1 0 1 0 1 0 0 1 ...
 $ Cancer       : int  0 0 0 0 0 0 0 0 0 1 ...
 $ Renal        : int  0 0 0 0 0 0 0 0 0 0 ...
 $ Infection    : int  1 0 0 1 1 1 0 0 0 0 ...
 $ CPR          : int  0 0 0 0 0 0 0 0 0 0 ...
 $ Systolic     : int  142 112 100 142 110 110 104 144 108 138 ...
 $ HeartRate    : int  88 80 70 103 154 132 66 110 60 103 ...
 $ Previous     : int  0 1 0 0 1 0 0 0 0 0 ...
 $ Type         : int  1 1 0 1 1 1 0 1 1 0 ...
 $ Fracture     : int  0 0 0 1 0 0 0 0 0 0 ...
 $ PO2          : int  0 0 0 0 0 1 0 0 0 0 ...
 $ PH           : int  0 0 0 0 0 0 0 0 0 0 ...
 $ PCO2         : int  0 0 0 0 0 0 0 0 0 0 ...
 $ Bicarbonate  : int  0 0 0 0 0 1 0 0 0 0 ...
 $ Creatinine   : int  0 0 0 0 0 0 0 0 0 0 ...
 $ Consciousness: int  1 1 1 1 1 1 1 1 1 1 ...

The ICU Admissions dataset consists of 200 observations with 21 variables. From these observations we found;

1. The dependent variable is the binary variable Vital Status (Status).
   
2. Nineteen possible predictor variables, both discrete and continuous, were also observed.
3. Most of the variables are integer but from information about the data, most of the variables can be recoded to factor variables. Several of the variables have two to three levels categories and so while they are numerical, their means do not offer any meaningful information.
4. There are only four variables that can be left as numerical variables others can be recoded to categorical/factor variables.
   
5. There are no missing data.

5.1 Converting Numerical Variables to Factor Variables

Attributes that could be recoded as factors included Status, Sex, Race, Service, Cancer, Renal, Infection, CPR, Previous, Type, Fracture, PCO2, PH, PO2, Bicarbonate, Creatinine and Consciousness. Labelling the factor levels with level names helps with comparative analysis and visualization.

> ICU <- within(ICU, {
+   Status <- factor(Status, labels=c('Lived','Died'))
+   Sex <- factor(Sex, labels=c('Male','Female'))
+   Race <- factor(Race, labels=c('White','Black','Other'))
+   Service <- factor(Service, labels=c('Medical','Surgical'))
+   Cancer <- factor(Cancer, labels=c('No','Yes'))
+   Renal <- factor(Renal, labels=c('No','Yes'))
+   Infection <- factor(Infection, labels=c('No','Yes'))
+   CPR <- factor(CPR, labels=c('No','Yes'))
+   Previous <- factor(Previous, labels=c('No','Yes'))
+   Type <- factor(Type, labels=c('Elective','Emergency'))
+   Fracture <- factor(Fracture, labels=c('No','Yes'))
+   PCO2 <- factor(PCO2, labels=c('No','Yes'))
+   PH <- factor(PH, labels=c('No','Yes'))
+   PO2 <- factor(PO2, labels=c('No','Yes'))
+   Bicarbonate <- factor(Bicarbonate, labels=c('No','Yes'))
+   Creatinine <- factor(Creatinine, labels=c('No','Yes'))
+   Consciousness <- factor(Consciousness, labels=c('Conscious','Deep Stupor','Coma'))
+ })

5.2 Recoding Numeric variables into bins

Several tests required recoding some of our numerical variables into bins. For Age, bins were created using equal count bins. Systolic was binned by blood pressure categories. HeartRate was also binned based on categories of bradycardia and elevated heart rate. the

Binning of the Age variable with equal-count bins:

> ICU$Age.binned <- 
+   with(ICU, binVariable(Age,
+    bins=5, method='proportions', 
+   labels=c('Group 1','Group 2','Group 3',
+   'Group 4','Group 5')))

Binning of the Systolic variable by hypotension and hypertension categories:

> ICU <- 
+   within(ICU, {
+   Systolic.grouped <- Recode(Systolic, 
+   '0:80="hypotension"; 80:120="normal"; 120:129="elevated"; 130:139="stage 1 hypertension"; 140:180="stage 2 hypertension"; 180:260="stage 3 hypertension"; ;',
+    as.factor=TRUE)
+ })

Binning of the HeartRate variable by groups of bradycardia, normal and elevated heart rate:

> ICU <- 
+   within(ICU, {
+   HeartRate.grouped <- Recode(HeartRate, 
+   '0:60="bradycardia"; 60:100="normal"; 100:200="elevated"',
+    as.factor=TRUE)
+ })

5.3 Saving Recoded Dataset

> # write.csv(ICU, file="ICUAdmissions_recoded.csv", row.names=FALSE)

6.1 Preview of Recoded Dataset

Below is a table containing results from the first and last four variables in this dataset.

> headTail(ICU) %>% datatable(rownames = TRUE, filter="top", options = list(pageLenght = 10, scrollX=T))%>% formatRound(columns=c(1:17), digits=0)

> str(ICU)

'data.frame':   200 obs. of  24 variables:
 $ ID               : int  8 12 14 28 32 38 40 41 42 50 ...
 $ Status           : Factor w/ 2 levels "Lived","Died": 1 1 1 1 1 1 1 1 1 1 ...
 $ Age              : int  27 59 77 54 87 69 63 30 35 70 ...
 $ Sex              : Factor w/ 2 levels "Male","Female": 2 1 1 1 2 1 1 2 1 2 ...
 $ Race             : Factor w/ 3 levels "White","Black",..: 1 1 1 1 1 1 1 1 2 1 ...
 $ Service          : Factor w/ 2 levels "Medical","Surgical": 1 1 2 1 2 1 2 1 1 2 ...
 $ Cancer           : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 2 ...
 $ Renal            : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 1 ...
 $ Infection        : Factor w/ 2 levels "No","Yes": 2 1 1 2 2 2 1 1 1 1 ...
 $ CPR              : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 1 ...
 $ Systolic         : int  142 112 100 142 110 110 104 144 108 138 ...
 $ HeartRate        : int  88 80 70 103 154 132 66 110 60 103 ...
 $ Previous         : Factor w/ 2 levels "No","Yes": 1 2 1 1 2 1 1 1 1 1 ...
 $ Type             : Factor w/ 2 levels "Elective","Emergency": 2 2 1 2 2 2 1 2 2 1 ...
 $ Fracture         : Factor w/ 2 levels "No","Yes": 1 1 1 2 1 1 1 1 1 1 ...
 $ PO2              : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 2 1 1 1 1 ...
 $ PH               : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 1 ...
 $ PCO2             : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 1 ...
 $ Bicarbonate      : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 2 1 1 1 1 ...
 $ Creatinine       : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 1 ...
 $ Consciousness    : Factor w/ 3 levels "Conscious","Deep Stupor",..: 1 1 1 1 1 1 1 1 1 1 ...
 $ Age.binned       : Factor w/ 5 levels "Group 1","Group 2",..: 1 3 5 2 5 4 3 1 1 4 ...
 $ Systolic.grouped : Factor w/ 6 levels "elevated","hypotension",..: 5 3 3 5 3 3 3 5 3 4 ...
 $ HeartRate.grouped: Factor w/ 3 levels "bradycardia",..: 3 3 3 2 2 2 3 2 1 2 ...

Findings

• The following variables were successfully recoded; Status, Sex, Race, Service, Cancer, Renal, Infection, CPR, Previous, Type,Fracture, PCO2,PH, PO2, Bicarbonate, Creatinine, and Consciousness.

6.2 Statistical Summary of the Recoded Dataset

> summary(ICU)

       ID          Status         Age            Sex         Race    
 Min.   :  4.0   Lived:160   Min.   :16.00   Male  :124   White:175  
 1st Qu.:210.2   Died : 40   1st Qu.:46.75   Female: 76   Black: 15  
 Median :412.5               Median :63.00                Other: 10  
 Mean   :444.8               Mean   :57.55                           
 3rd Qu.:671.8               3rd Qu.:72.00                           
 Max.   :929.0               Max.   :92.00                           
     Service    Cancer    Renal     Infection  CPR         Systolic    
 Medical : 93   No :180   No :181   No :116   No :187   Min.   : 36.0  
 Surgical:107   Yes: 20   Yes: 19   Yes: 84   Yes: 13   1st Qu.:110.0  
                                                        Median :130.0  
                                                        Mean   :132.3  
                                                        3rd Qu.:150.0  
                                                        Max.   :256.0  
   HeartRate      Previous         Type     Fracture   PO2        PH     
 Min.   : 39.00   No :170   Elective : 53   No :185   No :184   No :187  
 1st Qu.: 80.00   Yes: 30   Emergency:147   Yes: 15   Yes: 16   Yes: 13  
 Median : 96.00                                                          
 Mean   : 98.92                                                          
 3rd Qu.:118.25                                                          
 Max.   :192.00                                                          
  PCO2     Bicarbonate Creatinine     Consciousness   Age.binned
 No :180   No :185     No :190    Conscious  :185   Group 1:41  
 Yes: 20   Yes: 15     Yes: 10    Deep Stupor:  5   Group 2:39  
                                  Coma       : 10   Group 3:43  
                                                    Group 4:44  
                                                    Group 5:33  
                                                                
             Systolic.grouped   HeartRate.grouped
 elevated            :17      bradycardia: 15    
 hypotension         :12      elevated   : 80    
 normal              :61      normal     :105    
 stage 1 hypertension:30                         
 stage 2 hypertension:65                         
 stage 3 hypertension:15                         

6.3 Numerical Summary of Integer Variables

> numSummary(ICU[,c("Age", "HeartRate", "Systolic"), drop=FALSE], statistics=c("mean", "sd", "IQR", 
+   "quantiles"), quantiles=c(0,.25,.5,.75,1))

             mean       sd   IQR 0%    25% 50%    75% 100%   n
Age        57.545 20.05465 25.25 16  46.75  63  72.00   92 200
HeartRate  98.925 26.82962 38.25 39  80.00  96 118.25  192 200
Systolic  132.280 32.95210 40.00 36 110.00 130 150.00  256 200

Findings

• Age ranges from 16-92 years old with a mean of 57.55 and median of 63
• Systolic blood pressure ranges from 36-256 mmHg with a mean of 132.3 and median of 130
• Heart rate ranges from 39-192 beats per minute with a mean of 98.92 and median of 96

7.1 Examining the Variables Distribution

===========================================================================

   Variable   p_1 p_10   p_25  p_50   p_75  p_90   p_99
1  Systolic 55.92   92    110   130    150   170 212.12
2       Age 16.99   21  46.75    63     72    78     91
3 HeartRate 45.98   65     80    96 118.25 136.1 162.08
4        ID 11.96 81.3 210.25 412.5 671.75 829.8 924.01

Using the xray package, general trends in the dataset were identified.

1. There are more male observations in the dataset than females.

2. Many of the admissions to the ICU were emergencies, with a about a quarter of admissions being elective. This could relate to elective surgical procedures where morbidity could have been high or complications occurred. It is unclear whether people would be preemptively admitted to the ICU for high-risk procedures or if these elective admissions could be thought of as unforeseen or emergencies in themselves.

3. Looking at Status, more than 75% of observations lived after their ICU admission.

4. While the numbers are roughly even, slightly more procedures were surgical.

5. More admitted patients had no chronic renal failure, no previous admissions to the ICU, fracture, CPR or cancer when admitted. Most admitted patients had PO2 above or equal to 60, blood pH above or equal to 7.25, PCO2 below or equal to 45, and creatinine below or equal to 2. Much more of the observations were also white. Due to the large difference between groups some of these variables were not further explored, and the focus of exploratory data analysis and understanding of distribution was on variables where values might have been prior to admission. These might aid clinicians who work in the ICU in understanding the likelihood of survival for individuals who are admitted before lab work has been ordered.

6. Most patients admitted were conscious, with slighly more patients being comatose than in a deep stupor if unconscious.

7. Looking at histograms of the three numerical variables in the dataset, which were Age, Systolic and HeartRate, it could be guess that if any of the distributions were to be normal, they would be Systolic and HeartRate. Age is very obviously not normally distributed. Systolic looks like it is centered around 140, and the mean confirms this as mentioned above. The mean of HeartRate seems to be centered around 100 and its mean confirms this visual estimate.

7.2 Distribution of Vital Status by Factor Variables

> library(ggplot2)
> f01<-ggplot(ICU, aes(x=Sex, fill = Status)) +
+  theme_bw() +
+  geom_bar() +
+  labs(y = "Patient Count",
+       title = "Vital Status by Sex")
> 
> f02<-ggplot(ICU, aes(x=Race, fill = Status)) +
+  theme_bw() +
+  geom_bar() +
+  labs(y = "Patient Count",
+       title = "Vital Status by Race")
> f03<-ggplot(ICU, aes(x=Service, fill = Status)) +
+  theme_bw() +
+  geom_bar() +
+  labs(y = "Patient Count",
+       title = "Vital Status by Service")
> 
> f04<-ggplot(ICU, aes(x=Cancer, fill = Status)) +
+  theme_bw() +
+  geom_bar() +
+  labs(y = "Patient Count",
+       title = "Vital Status by Cancer")
> 
> library(Rmisc)
> multiplot(f01, f02, f03, f04,  layout=matrix(c(1:4), nrow=2, byrow=TRUE))

Observation

• Due to the increased ratio in the population ofmale to female, the ratio of the number of patients who lived is found almost directly proportional between male and female.
• From the graph regarding vital Status by race, it can be seen that the patient population of the White race is higher than the patient count for Black and other races. Overall, in the different races there are more cases of patients that lived than died.
• For the Vital status by Service, we can also observe that more patient died receiving medical service than surgical service.
• In the case of the Vital status by Cancer graph, there are more patients without a present case of Cancer, however there are als more patients who died and do not have a present case of Cancer.

> f05<-ggplot(ICU, aes(x=Renal, fill = Status)) +
+  theme_bw() +
+  geom_bar() +
+  labs(y = "Patient Count",
+       title = "Vital Status by Renal")
> 
> f06<-ggplot(ICU, aes(x=Infection, fill = Status)) +
+  theme_bw() +
+  geom_bar() +
+  labs(y = "Patient Count",
+       title = "Vital Status by Infection")
> 
> f07<-ggplot(ICU, aes(x=CPR, fill = Status)) +
+  theme_bw() +
+  geom_bar() +
+  labs(y = "Patient Count",
+       title = "Vital Status by CPR")
> 
> f08<-ggplot(ICU, aes(x=Previous, fill = Status)) +
+  theme_bw() +
+  geom_bar() +
+  labs(y = "Patient Count",
+       title = "Vital Status by Previous")
> 
> library(Rmisc)
> multiplot(f05, f06, f07, f08,  layout=matrix(c(1:4), nrow=2, byrow=TRUE))

Observation

• For the Vital Status by Renal, there are more patients without history of chronic Renal failure and most of then lived however, it is also observed that there seems to be an equal proportion in Status of patients who had an history with chronic Renal failure.
• In the case of Vital status by Infection, it can be observed that there are more cases of patients that lived than died regardless of if they have infection or not. However, there are more cases of patients who probably had infections and died.
• For the vital Status by CPR, it can be observed that there are more patients who were admitted in the ICU without prior CPR but there is the likelihood of patients dying with prior CPR.
• The visualization of Vital Status by Previous shows that there are more patients without previous ICU admission and the cases of patients who died was low.

> f09<-ggplot(ICU, aes(x=Type, fill = Status)) +
+  theme_bw() +
+  geom_bar() +
+  labs(y = "Patient Count",
+       title = "Vital Status by Type")
> 
> f10<-ggplot(ICU, aes(x=Fracture, fill = Status)) +
+  theme_bw() +
+  geom_bar() +
+  labs(y = "Patient Count",
+       title = "Vital Status by Fracture")
> 
> f11<-ggplot(ICU, aes(x=PO2, fill = Status)) +
+  theme_bw() +
+  geom_bar() +
+  labs(y = "Patient Count",
+       title = "Vital Status by PO2")
> 
> f12<-ggplot(ICU, aes(x=PH, fill = Status)) +
+  theme_bw() +
+  geom_bar() +
+  labs(y = "Patient Count",
+       title = "Vital Status by PH")
> 
> library(Rmisc)
> multiplot(f09, f10, f11, f12,  layout=matrix(c(1:4), nrow=2, byrow=TRUE))

Observation

• For the Vital Status by Type, there are more patients with emergency ICU admission and those also expereince more cases of death than the elective ICU admissions.
  
• In the case of Vital status by Fracture, it can be observed that there are more cases of patients that lived than died regardless of if they have Fracture or not.
  
• For the vital Status by PO2, it can be observed that there are more patients who were admitted in the ICU without PO2 but there is the likelihood of patients dying with having PO2.
  
• The visualization of Vital Status by PH shows that there are more patients without a dangerous level of PH and the cases of patients who died was low.

> f13<-ggplot(ICU, aes(x=PCO2, fill = Status)) +
+  theme_bw() +
+  geom_bar() +
+  labs(y = "Patient Count",
+       title = "Vital Status by PCO2")
> 
> f14<-ggplot(ICU, aes(x=Bicarbonate, fill = Status)) +
+  theme_bw() +
+  geom_bar() +
+  labs(y = "Patient Count",
+       title = "Vital Status by Bicarbonate")
> 
> f15<-ggplot(ICU, aes(x=Creatinine, fill = Status)) +
+  theme_bw() +
+  geom_bar() +
+  labs(y = "Patient Count",
+       title = "Vital Status by Creatinine")
> 
> f16<-ggplot(ICU, aes(x=Consciousness, fill = Status)) +
+  theme_bw() +
+  geom_bar() +
+  labs(y = "Patient Count",
+       title = "Vital Status by Consciousness")
> 
> 
> library(Rmisc)
> multiplot(f13, f14, f15, f16, layout=matrix(c(1:4), nrow=2, byrow=TRUE))

Observations

From the collection of graphs above, the most visually prominent chart is the relationship between vital status and Consciousness which shows that although there is a high count of patients who were conscious at admission, however most patients that were received at a stage of Deep Stupor or Coma lost consciousness and died.

10.1 Cancer by Age

There are three peaks for Ages where ICU admissions involved cancer. These are around 20, 50 and 70 years of age. Given the relatively small number of individuals who had cancer involvement with their admission, and the variability in ages associated, cancer might not be the best predictor of ICU admission.

> ggplot(ICU, aes(x=Age, fill = Cancer)) +
+   theme_bw() +
+       geom_density(alpha=0.5) +
+   labs(y = "Density",
+        title = "Density distribution of Cancer by Age")

Difference in Means

H0: the variances for admissions involving cancer and admission not involving cancer are equal
Ha: the variances are different

H0: the means are equal
Ha: the means are different

The following is the comparison of means and variances of Age by Cancer.

> numSummary(ICU[,c("Age"), drop=FALSE], groups=ICU$Cancer, statistics=c("mean","sd", "se(mean)"), quantiles=c(0,.25,.5,.75,1))

        mean       sd se(mean) Age:n
No  57.70556 20.30953 1.513783   180
Yes 56.10000 17.99971 4.024857    20

Since the p-value = 0.5684 for testing the homogeneity of variances is greater than 0.05, we retain the null hypothesis with a 5% risk of a type 1 error and conclude that the variances for admissions involving cancer vs those that do not are equal. As such, the Student t-test is used to analyze whether there was a significant difference in means.

> leveneTest(Age ~ Cancer, data=ICU, center="median")

Levene's Test for Homogeneity of Variance (center = "median")
       Df F value Pr(>F)
group   1  0.3265 0.5684
      198               

As the p-value = 0.735, 0 is within the confidence intervals of -7.736825 to 10.947937 and t = 0.33891 is less than 1.971957, we retain the null hypothesis at a 5% risk level of a type 1 error and conclude that the means for age are the same between the two groups.

> t.test(Age~Cancer, alternative='two.sided', conf.level=.95, var.equal=TRUE, data=ICU)

    Two Sample t-test

data:  Age by Cancer
t = 0.33891, df = 198, p-value = 0.735
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -7.736825 10.947937
sample estimates:
 mean in group No mean in group Yes 
         57.70556          56.10000 

10.2 Infection by Age

ICU admissions that involved infection centered around 60-65 years of age. This association is relatively clear visually looking at the plot below.

> ggplot(ICU, aes(x=Age, fill = Infection )) +
+   theme_bw() +
+       geom_density(alpha=0.5) +
+   labs(y = "Density",
+        title = "Density distribution of Infection by Age")

Difference in Means

H0: the variances for admissions involving infection and those that do not are equal
Ha: the variances are different

H0: the means are equal
Ha: the means are different

The following is the comparison of means and variances of Age by Infection.

> numSummary(ICU[,c("Age"), drop=FALSE], groups=ICU$Infection, statistics=c("mean","sd", "se(mean)"), quantiles=c(0,.25,.5,.75,1))

        mean       sd se(mean) Age:n
No  54.93103 21.21842 1.970081   116
Yes 61.15476 17.82545 1.944917    84

Since the p-value = 0.04162 for testing the homogeneity of variances is less than 0.05, we reject the null hypothesis with a 5% risk of a type 1 error and conclude that the variances for admissions involving infection and admissions not involving infection are not equal. As such, the Welch two sample t-test is used to analyze whether there was a significant difference in means.

> leveneTest(Age ~ Infection, data=ICU, center="median")

Levene's Test for Homogeneity of Variance (center = "median")
       Df F value  Pr(>F)  
group   1  4.2053 0.04162 *
      198                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

As the p-value = 0.02569, 0 is not within the confidence intervals of -11.6837808 to -0.7636741 and t = -2.2481 is less than -1.971957, we reject the null hypothesis at a 5% risk level of a type 1 error and conclude that the means for age are not the same between the two groups. this suggests that there may be a relationship between Age and Infection.

> t.test(Age~Infection, alternative="two.sided", conf.level=.95, var.equal=FALSE, data=ICU)

    Welch Two Sample t-test

data:  Age by Infection
t = -2.2481, df = 193.6, p-value = 0.02569
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -11.6837808  -0.7636741
sample estimates:
 mean in group No mean in group Yes 
         54.93103          61.15476 

10.3 Consciousness by Age

Another association that was explored was between Age and Consiousness. All three categories for Consciousness overlap with peaks between 50 and 75 years of age. There is a distinct peak at around 50 for deep stupor, indicating that this age might be associated with deep stupor when related to ICU admissions. However, deep stupor also has a secondary peak at around 75, which make it less clearly how this consciousness category relates to age in this dataset.

> ggplot(ICU, aes(x=Age, fill = Consciousness )) +
+   theme_bw() +
+       geom_density(alpha=0.5) +
+   labs(y = "Density",
+        title = "Density distribution of Consciousness by Age")

Difference in Means (ANOVA)

H0: the variances for Age is the same across all levels of consciousness
Ha: the variances are different

H0: the means are equal
Ha: the means are different

The following is the comparison of means and variances of Age by Consciousness.

> numSummary(ICU[,c("Age"), drop=FALSE], groups=ICU$Consciousness, statistics=c("mean","sd", "se(mean)"), quantiles=c(0,.25,.5,.75,1))

                mean       sd se(mean) Age:n
Conscious   57.02162 20.50927 1.507871   185
Deep Stupor 61.20000 11.16692 4.993996     5
Coma        65.40000 12.50067 3.953058    10

Testing normality
H0: the several distributions are normally distributed
Ha: the distributions are not normally distributed

According the q-q plot and Shapiro-Wilk normality test for each of the three levels of consciousness, Age does not appear to be normally distributed for the level of consciousness = conscious. This was found as the q-q plot for conscious does not follow the diagonal line and the p-value = 5.319e-08 which is less than 0.05. Additionally, based on the normality test previously performed on Age, the p-value = 2.507e-08 which is less than 0.05. As such, we would reject the null hypothesis at a 5% risk and conclude that the distributions are not normally distributed. That being said, since normality was rejected, the Kruskal-Wallis test should be used to determine whether the four distributions are the same.

> with(ICU, qqPlot(Age, dist="norm", id=list(method="y", n=2, 
+   labels=rownames(ICU)), groups=Consciousness))

> normalityTest(Age ~ Consciousness, test="shapiro.test", data=ICU)

 --------
 Consciousness = Conscious 

    Shapiro-Wilk normality test

data:  Age
W = 0.92706, p-value = 5.319e-08

 --------
 Consciousness = Deep Stupor 

    Shapiro-Wilk normality test

data:  Age
W = 0.9012, p-value = 0.4165

 --------
 Consciousness = Coma 

    Shapiro-Wilk normality test

data:  Age
W = 0.96128, p-value = 0.8003

 --------

 p-values adjusted by the Holm method:
            unadjusted adjusted  
Conscious   5.3186e-08 1.5956e-07
Deep Stupor 0.41654    0.83308   
Coma        0.80031    0.83308   

Testing for Homogeneity of Variances
H0: variances are homogenous
Ha: at least one of the variances is different from the others

As the Levene Test generated a p-value = 0.0942, we would retain the null hypothesis with a 5% risk of a Type 1 error. This means that the difference in variances of Age for the different levels of consciousness is zero, and that the variances are homogeneous.

> leveneTest(Age ~ Consciousness, data=ICU , center=median)

Levene's Test for Homogeneity of Variance (center = median)
       Df F value Pr(>F)  
group   2  2.3909 0.0942 .
      197                 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Non-parametric Kruskal-Wallis test
As ‘normality’ was rejected, the Kruskal-Wallis test will be used in order to determine whether the three distributions for Age are the same.

The Kruskal-Wallis test produced a p-value of p-value = 0.6468, which is greater than 0.05. As such, we would retain the null hypothesis and conclude that the distributions are the same and that the means are likely the same.

> kruskal.test(Age ~ Consciousness, data=ICU)

    Kruskal-Wallis rank sum test

data:  Age by Consciousness
Kruskal-Wallis chi-squared = 0.87135, df = 2, p-value = 0.6468

10.4 Type by Age

Both admission Types, elective and emergency, happen more frequently with advancing age. However, elective admissions happen more frequently with older age. This might suggest that older individuals are more likely to have complications during surgical or other procedures that would require admissions to an intensive care unit. Depending on organizational policy or practice, this might also mean that individuals at the study site were premptively admitted to ICU, perhaps more frequently with advancing age, for fear of complications.

> ggplot(ICU, aes(x=Age, fill = Type )) +
+   theme_bw() +
+       geom_density(alpha=0.5) +
+   labs(y = "Density",
+        title = "Density distribution of Type by Age")

Difference in Means

H0: the variances for elective and emergency are equal
Ha: the variances are different

H0: the means are equal
Ha: the means are different

The following is the comparison of means and variances of Age by Type.

> numSummary(ICU[,c("Age"), drop=FALSE], groups=ICU$Type, statistics=c("mean","sd", "se(mean)"), quantiles=c(0,.25,.5,.75,1))

              mean       sd se(mean) Age:n
Elective  63.77358 15.49769 2.128772    53
Emergency 55.29932 21.05909 1.736924   147

Since the p-value = 0.001188 for testing the homogeneity of variances is less than 0.05, we reject the null hypothesis with a 5% risk of a type 1 error and conclude that the variances for elective and emergency admission types are not equal. As such, the Welch two sample t-test is used to analyze whether there was a significant difference in means.

> leveneTest(Age ~ Type, data=ICU, center="median")

Levene's Test for Homogeneity of Variance (center = "median")
       Df F value   Pr(>F)   
group   1  10.821 0.001188 **
      198                    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

As the p-value = 0.002513, 0 is not within the confidence intervals of 3.036522 to 13.912009 and t = 3.0844 is greater than 1.971957, we reject the null hypothesis at a 5% risk level of a type 1 error and conclude that the means for age are not the same between the two groups. This further confirms our observations from the graph that there is a difference between the two. Additionally, a relationship may exist between Age and admission type.

> t.test(Age~Type, alternative="two.sided", conf.level=.95, var.equal=FALSE, data=ICU)

    Welch Two Sample t-test

data:  Age by Type
t = 3.0844, df = 124.61, p-value = 0.002513
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
  3.036522 13.912009
sample estimates:
 mean in group Elective mean in group Emergency 
               63.77358                55.29932 

10.5 Service by Age

While the peaks for surgical and medical Service by Age overlap considerably, there is interestingly a peak of surgical service type in younger age groups, around 20 years of age. While it is not known what conditions led to these individuals being admitted, it might be concluded that older individuals would have more events that were related to their medication or needing medication, for example falls or stroke. This is a very weak conclusion to draw from the graph below, but if specific reasons for admission were also collected, this theory could be explored.

> ggplot(ICU, aes(x=Age, fill = Service)) +
+   theme_bw() +
+       geom_density(alpha=0.5) +
+   labs(y = "Density",
+        title = "Density distribution of Service by Age")

Difference in Means

H0: the variances for medical and surgical are equal
Ha: the variances are different

H0: the means are equal
Ha: the means are different

The following is the comparison of means and variances of Age by Service.

> numSummary(ICU[,c("Age"), drop=FALSE], groups=ICU$Service, statistics=c("mean","sd", "se(mean)"), quantiles=c(0,.25,.5,.75,1))

             mean       sd se(mean) Age:n
Medical  57.45161 18.56511 1.925112    93
Surgical 57.62617 21.35174 2.064150   107

Since the p-value = 0.2151 for testing the homogeneity of variances is greater than 0.05, we retain the null hypothesis with a 5% risk of a type 1 error and conclude that the variances for medical and surgical are equal. As such, the Student two t-test is used to analyze whether there was a significant difference in means.

> leveneTest(Age ~ Service, data=ICU, center="median")

Levene's Test for Homogeneity of Variance (center = "median")
       Df F value Pr(>F)
group   1  1.5464 0.2151
      198               

As the p-value = 0.9512, 0 is within the confidence intervals of -5.795344 to 5.446234 and t = -0.061242 is greater than -1.971957, we retain the null hypothesis at a 5% risk level of a type 1 error and conclude that the means for age are the same between the two groups.

> t.test(Age~Service, alternative='two.sided', conf.level=.95, var.equal=TRUE, data=ICU)

    Two Sample t-test

data:  Age by Service
t = -0.061242, df = 198, p-value = 0.9512
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -5.795344  5.446234
sample estimates:
 mean in group Medical mean in group Surgical 
              57.45161               57.62617 

10.6 Previous by Age

There is a definite an almost independent peak of history of previous ICU admission with older age. It can be noted that there is a smaller peak of relatively older individuals who were admitted who had not had a previous ICU admission within the past 6 months. This indicates that old age does not relate clearly to previous ICU admission and future ICU admission. On the extremes of age, younger individuals are shown to have less frequency of previous ICU admission within the past 6 months, while there is a small peak of older admission of the individuals in this dataset having had a previous ICU admission in the past 6 months. There might be a smaller increased likelihood of ICU admission with previous ICU admission in the past 6 months with age.

> ggplot(ICU, aes(x=Age, fill = Previous )) +
+   theme_bw() +
+       geom_density(alpha=0.5) +
+   labs(y = "Density",
+        title = "Density distribution of Previous by Age")

Difference in Means

H0: the variances for previous admission within the past 6 months and no previous admission within the past 6 months are equal
Ha: the variances are different

H0: the means are equal
Ha: the means are different

The following is the comparison of means and variances of Age by Previous.

> numSummary(ICU[,c("Age"), drop=FALSE], groups=ICU$Previous, statistics=c("mean","sd", "se(mean)"), quantiles=c(0,.25,.5,.75,1))

        mean       sd se(mean) Age:n
No  56.96471 20.69528 1.587256   170
Yes 60.83333 15.83554 2.891161    30

Since the p-value = 0.05185 for testing the homogeneity of variances is greater than 0.05, we retain the null hypothesis with a 5% risk of a type 1 error and conclude that the variances for previous admission within the past 6 months and no previous admission within the past 6 months are equal. As such, the Student two t-test is used to analyze whether there was a significant difference in means.

> leveneTest(Age ~ Previous, data=ICU, center="median")

Levene's Test for Homogeneity of Variance (center = "median")
       Df F value  Pr(>F)  
group   1  3.8268 0.05185 .
      198                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

As the p-value = 0.3312, 0 is within the confidence intervals of -11.701332 to 3.964077 and t = -0.97399 is greater than -1.971957, we retain the null hypothesis at a 5% risk level of a type 1 error and conclude that the means for age are the same between the two groups.

> t.test(Age~Previous, alternative='two.sided', conf.level=.95, var.equal=TRUE, data=ICU)

    Two Sample t-test

data:  Age by Previous
t = -0.97399, df = 198, p-value = 0.3312
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -11.701332   3.964077
sample estimates:
 mean in group No mean in group Yes 
         56.96471          60.83333 

10.7 Renal by Age

The plot of density distribution of the two renal categories by Age indicates that both Status groups had a higher frequency of chronic renal failure as age progressed, and peaked at around 70-75 years of age. There is a small peaks at 20 and a smaller peak at about 30 years of age for individuals who did not have chronic renal failure and did have chronic renal failure on admission, respectively. The amount of overlap in the peaks confirms the results of the previous table above indicating that the Renal attribute might not give more insight into ICU outcomes.

> ggplot(ICU, aes(x=Age, fill = Renal )) +
+   theme_bw() +
+       geom_density(alpha=0.5) +
+   labs(y = "Density",
+        title = "Density distribution of Renal by Age")

Difference in Means
H0: the variances for history of chronic renal failure and no history Ha: the variances are different

H0: the means are equal
Ha: the means are different

The following is the comparison of means and variances between the history of chronic renal failue and no history for Age.

> numSummary(ICU[,c("Age"), drop=FALSE], groups=ICU$Renal, statistics=c("mean","sd", "se(mean)"), quantiles=c(0,.25,.5,.75,1))

        mean       sd se(mean) Age:n
No  56.53039 20.28315 1.507634   181
Yes 67.21053 14.94649 3.428961    19

Since the p-value = 0.1385 for testing the homogeneity of variances is greater than 0.05, we retain the null hypothesis with a 5% risk of a type 1 error and conclude that the variances for history and no history are equal. As such, the Student t-test is used to analyze whether there was a significant difference in means.

> leveneTest(Age ~ Renal, data=ICU, center="median")

Levene's Test for Homogeneity of Variance (center = "median")
       Df F value Pr(>F)
group   1  2.2128 0.1385
      198               

As the p-value = 0.02685, 0 is not within the confidence intervals of -20.123596 to -1.236684 and t = -2.2303 is less than -1.971957, we reject the null hypothesis at a 5% risk level of a type 1 error and conclude that the means for Renal are not the same between the two groups.

> t.test(Age~Renal, alternative='two.sided', conf.level=.95, var.equal=TRUE, data=ICU)

    Two Sample t-test

data:  Age by Renal
t = -2.2303, df = 198, p-value = 0.02685
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -20.123596  -1.236684
sample estimates:
 mean in group No mean in group Yes 
         56.53039          67.21053 

10.8 Sex by Age

From the plot below, it seems that females who were admitted to the ICU were older than their male counterparts. There are similar peaks and patterns for younger individuals: females were older if admitted to ICU than their male counterparts.

> ggplot(ICU, aes(x=Age, fill = Sex)) +
+   theme_bw() +
+       geom_density(alpha=0.5) +
+   labs(y = "Density",
+        title = "Density distribution of Sex by Age")

Difference in Means
H0: the variances for Males and Females are equal
Ha: the variances are different

H0: the means are equal
Ha: the means are different

The following is the comparison of means and variances between the two Males and Females for Age.

> numSummary(ICU[,c("Age"), drop=FALSE], groups=ICU$Sex, statistics=c("mean","sd", "se(mean)"), quantiles=c(0,.25,.5,.75,1))

           mean       sd se(mean) Age:n
Male   56.04032 19.45451 1.747067   124
Female 60.00000 20.89466 2.396781    76

Since the p-value = 0.7344 for testing the homogeneity of variances is greater than 0.05, we retain the null hypothesis with a 5% risk of a type 1 error and conclude that the variances for Males and Females are equal. As such, the Student t-test is used to analyze whether there was a significant difference in means.

> leveneTest(Age ~ Sex, data=ICU, center="median")

Levene's Test for Homogeneity of Variance (center = "median")
       Df F value Pr(>F)
group   1  0.1154 0.7344
      198               

As the p-value = 0.1759, 0 is within the confidence intervals of -9.708824 to 1.789469 and t = -1.3582 is greater than -1.971957, we retain the null hypothesis at a 5% risk level of a type 1 error and conclude that the means for Age are the same between the two groups. This further confirms our observations from the graph that the peaks of the two sexes are similar.

> t.test(Age~Sex, alternative='two.sided', conf.level=.95, var.equal=TRUE, data=ICU)

    Two Sample t-test

data:  Age by Sex
t = -1.3582, df = 198, p-value = 0.1759
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -9.708824  1.789469
sample estimates:
  mean in group Male mean in group Female 
            56.04032             60.00000 

10.9 Vital Status by Age

Overlaying Status and Age, density plots show that deaths after admission follow the larger Age peak that contains middle aged to elderly individuals.

> ggplot(ICU, aes(x=Age, fill = Status)) +
+   theme_bw() +
+       geom_density(alpha=0.5) +
+   labs(y = "Density",
+        title = "Density distribution of Vital Status by Age")

When the additional layer of Status, more information can be gathered from the relationship between Age and Sex. When looking at males, older males more often died than younger males, with similar frequency in advanced age, around the age of 65-70. In younger males, those admitted to the ICU were more often to have lived through their admission, where the opposite is seen in older males.

In females, there is a clearer distribution of older individuals who had died. No females in this dataset under the age of about 40 died on ICU admission. There is a clear peak at around 75 years and a smaller peak at around 50 of females who died on ICU admission. There is a higher frequency of younger females who lived through ICU admission, but there remains a higher frequency of women who were older in this group.

> ggplot(ICU, aes(x=Age, fill = Status)) +
+    theme_bw() +
+    facet_wrap(~ Sex) +
+        geom_density(alpha=0.5) +
+    labs(y = "Density",
+         title = "Density distribution of Vital Status in male and female patients by Age")

Difference in Means
H0: the variances for Lived and Died are equal
Ha: the variances are different

H0: the means are equal
Ha: the means are different

The following is the comparison of means and variances between the two Status groups for Age.

> numSummary(ICU[,c("Age"), drop=FALSE], groups=ICU$Status, statistics=c("mean","sd", "se(mean)"), quantiles=c(0,.25,.5,.75,1))

        mean       sd se(mean) Age:n
Lived 55.650 20.42818 1.614990   160
Died  65.125 16.64900 2.632438    40

Since the p value = 0.07855 for testing the homogeneity of variances is greater than 0.05, we retain the null hypothesis with a 5% risk of a type 1 error and conclude that the variances for Lived and Died are equal. As such, the Student t-test is used to analyze whether there was a significant difference in means.

> leveneTest(Age ~ Status, data=ICU, center="median")

Levene's Test for Homogeneity of Variance (center = "median")
       Df F value  Pr(>F)  
group   1   3.127 0.07855 .
      198                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

As the p-value = 0.007211, 0 is not within the confidence intervals of -16.35688 to -2.59312 and t = -2.7151 is less than -1.971957, we reject the null hypothesis and conclude that the means for Age for the groups Lived and Died are not the same. This suggests that there might be a relationship between Age and Vital Status.

> t.test(Age~Status, alternative='two.sided', conf.level=.95, var.equal=TRUE, data=ICU)

    Two Sample t-test

data:  Age by Status
t = -2.7151, df = 198, p-value = 0.007211
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -16.35688  -2.59312
sample estimates:
mean in group Lived  mean in group Died 
             55.650              65.125 

11.1 Vital Status by Heart Rate

Both status categories have similar peaks when plotted on a density estimate plot of HeartRate. This indicates that there might not be a difference in the Status response category based on HeartRate. People who lived did seem to have a higher density of HeartRate values around 90 than those who died. A normal adult heart rate ranges between 60 and 100 beats per minute. This graph might suggest that people who lived more often had heart rates within this range, whereas those who died seemed more likely to have higher heartrates. This could inform further analysis or research.

> ggplot(ICU, aes(x=HeartRate, fill = Status)) +
+   theme_bw() +
+       geom_density(alpha=0.5) +
+   labs(y = "Density",
+        title = "Density distribution of Vital Status by HeartRate")

Difference in Means
H0: the variances for Lived and Died are equal
Ha: the variances are different

H0: the means are equal
Ha: the means are different

The following is the comparison of means and variances between the two Status groups for HeartRate.

> numSummary(ICU[,c("HeartRate"), drop=FALSE], groups=ICU$Status, statistics=c("mean","sd", "se(mean)"), quantiles=c(0,.25,.5,.75,1))

         mean       sd se(mean) HeartRate:n
Lived  98.500 26.97868 2.132852         160
Died  100.625 26.49304 4.188918          40

Since the p-value = 0.929 for testing the homogeneity of variances is greater than 0.05, we retain the null hypothesis with a 5% risk of a type 1 error and conclude that the variances for Lived and Died are equal. As such, the Student t-test is used to analyze whether there was a significant difference in means.

> leveneTest(HeartRate ~ Status, data=ICU, center="median")

Levene's Test for Homogeneity of Variance (center = "median")
       Df F value Pr(>F)
group   1   0.008  0.929
      198               

As the p-value = 0.6553, 0 is within the confidence intervals of -11.496845 to 7.246845 and t = -0.44714 is greater than -1.971957, we retain the null hypothesis at a 5% risk level of a type 1 error and conclude that the means for HeartRate are the same among those that lived and those that died. While observations from the graph suggest that people who lived more often had heart rates that were lower, based on the t-test, the means of the two groups are not statistically different.

> t.test(HeartRate~Status, alternative='two.sided', conf.level=.95, var.equal=TRUE, data=ICU)

    Two Sample t-test

data:  HeartRate by Status
t = -0.44714, df = 198, p-value = 0.6553
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -11.496845   7.246845
sample estimates:
mean in group Lived  mean in group Died 
             98.500             100.625 

12.1 Vital Status by Systolic

The distribution of Systolic values for those who died seem to be concentrated around 75 mmHg and 140mmHg. A normal Systolic blood pressure can vary widely but the American Heart Association states that blood pressure below 120mmHg is normal. However, excessively low blood pressure could be a result of bleeding, for example, and can result in insufficient blood flow to critical organs. Medications used to restore blood pressure are used when blood pressure becomes too low. This might explain the peak around 75mmHg in the death curve in the graph below.

> ggplot(ICU, aes(x=Systolic, fill = Status)) +
+   theme_bw() +
+       geom_density(alpha=0.5) +
+   labs(y = "Density",
+        title = "Density distribution of Vital Status Systolic")

Difference in Means
H0: the variances for Lived and Died are equal
Ha: the variances are different

H0: the means are equal
Ha: the means are different

The following is the comparison of variances between the two Status groups for Systolic.

> numSummary(ICU[,c("Systolic"), drop=FALSE], groups=ICU$Status, statistics=c("mean","sd", "se(mean)"), quantiles=c(0,.25,.5,.75,1))

          mean       sd se(mean) Systolic:n
Lived 135.6438 29.80151 2.356016        160
Died  118.8250 41.08084 6.495451         40

Since the p-value = 0.04205 for testing the homogeneity of variances is less than 0.05, we reject the null hypothesis with a 5% risk of a type 1 error and conclude that the variances for Lived and Died are not equal. As such, the Welch two Sample t-test is used to analyze whether there was a significant difference in means.

> leveneTest(Systolic ~ Status, data=ICU, center="median")

Levene's Test for Homogeneity of Variance (center = "median")
       Df F value  Pr(>F)  
group   1  4.1872 0.04205 *
      198                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

As the p-value = 0.01856, 0 is not within the confidence intervals of 2.938642 to 30.698858 and t = 2.4341 is greater than 1.971957, we reject the null hypothesis at a 5% risk level of a type 1 error and conclude that the means for systolic blood pressure are not the same among those that lived and those that died. As such, this might suggest that patients who lived had different systolic blood pressures compared to those that died. Therefore a relationship might exist between systolic blood pressure and vital status.

> t.test(Systolic~Status, alternative="two.sided", conf.level=.95, var.equal=FALSE, data=ICU)

    Welch Two Sample t-test

data:  Systolic by Status
t = 2.4341, df = 49.726, p-value = 0.01856
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
  2.938642 30.698858
sample estimates:
mean in group Lived  mean in group Died 
           135.6438            118.8250 

13.1 Vital status by Service

H0: there is no difference between the proportion of patients that died in the medical versus surgical group, risk = 0.05
Ha: there is a difference between the proportion of patients that died in the medical versus surgical group

The following code produces a crosstab of the proportions of Service (Medical and Surgical) by Status (Lived or Died).

> pacman::p_load(sjPlot)
> sjt.xtab(ICU$Status, ICU$Service, show.col.prc = TRUE)

The following code conducts a z-test and produces a z-value and a p-value for Service.

> x1<-26; x2<-14; n1<-93; n2<-107
> p1<-x1/n1; p2<-x2/n2
> p<-(x1+x2)/(n1+n2)  
> varp<-p*(1-p)*(1/n1 + 1/n2)  
> stdp<-sqrt(varp)  
> zp<-(p1 - p2)/stdp 
> zp

[1] 2.622729

> 1-pnorm(zp)

[1] 0.004361436

When conducting a two-tail z-test with a 5% level of risk of a type 1 error, the critical values are -1.96 and +1.96. The z-value of 2.622729 does not fall within this confidence interval, thus we reject the null hypothesis that there is no difference between the proportion of patients dying in the ICU from medical procedures versus surgical procedures.

Further, since the p-value of 0.004361436 is less than 0.05, we, again, reject the null hypothesis that the proportions of the two groups are equal.

Lastly, we can see from the table that more of those that died were there for a medical service and more of those that lived were there for a surgical service.

13.2 Vital status by Sex

H0: there is no difference between the proportion of male and female patients that died, risk = 0.05 Ha: there is a difference between the proportion of male and female patients that died

The following code produces a crosstab of the proportions of Sex (Male and Female) by Status (Lived or Died).

> pacman::p_load(sjPlot)
> sjt.xtab(ICU$Status, ICU$Sex, show.col.prc = TRUE)

The following code conducts a z-test and produces a z-value and a p-value for Sex.

> x1<-24; x2<-16; n1<-124; n2<-76
> p1<-x1/n1; p2<-x2/n2
> p<-(x1+x2)/(n1+n2)  
> varp<-p*(1-p)*(1/n1 + 1/n2)  
> stdp<-sqrt(varp)  
> zp<-(p1 - p2)/stdp 
> zp

[1] -0.2913583

> 1-pnorm(zp)

[1] 0.6146113

When conducting a two-tail z-test with a 5% level of risk of a type 1 error, the critical values are -1.96 and +1.96. The z-value of -0.2913583 does fall within this confidence interval, thus we fail to reject the null hypothesis that there is no difference between the proportion of male and female patients that died in the ICU.

Further, since the p-value of 0.6146113 is greater than 0.05, we, again, fail to reject the null hypothesis that the proportions of the two groups are equal.

Thus, the proportion of men and women that died in the ICU was equal.

We would, however, like to note that there are significantly more males in this dataset than females, which reduces the integrity of the analysis.

13.3 Vital status by Infection

H0: there is no difference between the proportion of infection probable versus non-infection probable carrying patients that died, risk = 0.05 Ha: there is a difference between the proportion of infection probable versus non-infection probable carrying patients that died

The following code produces a crosstab of the proportions of Infection (No and Yes) by Status (Lived or Died).

> pacman::p_load(sjPlot)
> sjt.xtab(ICU$Status, ICU$Infection, show.col.prc = TRUE)

The following code conducts a z-test and produces a z-value and a p-value for Infection.

> x1<-16; x2<-24; n1<-116; n2<-84
> p1<-x1/n1; p2<-x2/n2
> p<-(x1+x2)/(n1+n2)  
> varp<-p*(1-p)*(1/n1 + 1/n2)  
> stdp<-sqrt(varp)  
> zp<-(p1 - p2)/stdp 
> zp

[1] -2.578807

> 1-pnorm(zp)

[1] 0.9950429

When conducting a two-tail z-test with a 5% level of risk of a type 1 error, the critical values are -1.96 and +1.96. The z-value of -2.578807 does not fall within this confidence interval, thus we fail to reject the null hypothesis that there is no difference between the proportion of infection probable versus non-infection probable patients that died.

Further, since the p-value of 0.9950429 is greater than 0.05, we, again, fail to reject the null hypothesis that the proportions of the two groups are equal.

Thus, the proportion of deaths in the infection probable patients is equal to the proportion of deaths in the non-infection probable patients.

13.4 Vital status by Renal

H0: there is no difference between the proportion of patients that died with a history of chronic renal failure versus without, risk = 0.05 Ha: there is a difference between the proportion of patients that died with a history of chronic renal failure versus without

The following code produces a crosstab of the proportions of Renal (No and Yes) by Status (Lived or Died).

> pacman::p_load(sjPlot)
> sjt.xtab(ICU$Status, ICU$Renal, show.col.prc = TRUE)

The following code conducts a z-test and produces a z-value and a p-value for Renal.

> x1<-32; x2<-8; n1<-181; n2<-19
> p1<-x1/n1; p2<-x2/n2
> p<-(x1+x2)/(n1+n2)  
> varp<-p*(1-p)*(1/n1 + 1/n2)  
> stdp<-sqrt(varp)  
> zp<-(p1 - p2)/stdp 
> zp

[1] -2.532143

> 1-pnorm(zp)

[1] 0.9943316

When conducting a two-tail z-test with a 5% level of risk of a type 1 error, the critical values are -1.96 and +1.96. The z-value of -2.532143 does not fall within this confidence interval, thus we fail to reject the null hypothesis that there is no difference between the proportion of patients that died with a history of chronic renal failure versus without.

Further, since the p-value of 0.9943316 is greater than 0.05, we, again, fail to reject the null hypothesis that the proportions of the two groups are equal.

Thus, the proportion of deaths in patients with a history of chronic renal failure is equal to the proportion of deaths in patients with no history of chronic renal failure.

13.5 Vital Status by CPR

H0: there is no difference between the proportion of deaths in patients who recieved CPR upon admission versus patients who did not, risk = 0.05 Ha: there is a difference between the proportion of deaths in patients who recieved CPR upon admission versus patients who did not

The following code produces a crosstab of the proportions of CPR (No and Yes) by Status (Lived or Died).

> pacman::p_load(sjPlot)
> sjt.xtab(ICU$Status, ICU$CPR, show.col.prc = TRUE)

The following code conducts a z-test and produces a z-value and a p-value for CPR.

> x1<-33; x2<-7; n1<-187; n2<-13
> p1<-x1/n1; p2<-x2/n2
> p<-(x1+x2)/(n1+n2)  
> varp<-p*(1-p)*(1/n1 + 1/n2)  
> stdp<-sqrt(varp)  
> zp<-(p1 - p2)/stdp 
> zp

[1] -3.155115

> 1-pnorm(zp)

[1] 0.9991978

When conducting a two-tail z-test with a 5% level of risk of a type 1 error, the critical values are -1.96 and +1.96. The z-value of -3.155115 does not fall within this confidence interval, thus we fail to reject the null hypothesis that there is no difference between the proportion of deaths in patients who recieved CPR upon admission versus patients who did not.

Further, since the p-value of 0.9991978 is greater than 0.05, we, again, fail to reject the null hypothesis that the proportions of the two groups are equal.

Thus, the proportion of deaths in patients who recieved CPR upon admission is equal to the proportion of deaths in patients who did not recieve CPR upon admission.

13.6 Vital status by Cancer

H0: there is no difference between the proportions of patients that died in the cancer versus non-cancer group, risk = 0.05
Ha: there is a difference between the proportions of patients that died in the cancer versus non-cancer group

The following code produces a crosstab of the proportions of Cancer (No and Yes) by Status (Lived or Died).

> pacman::p_load(sjPlot)
> sjt.xtab(ICU$Status, ICU$Cancer, show.col.prc = TRUE)

The following code conducts a z-test and produces a z-value and a p-value for Cancer.

> x1<-36; x2<-4; n1<-180; n2<-20
> p1<-x1/n1; p2<-x2/n2
> p<-(x1+x2)/(n1+n2)  
> varp<-p*(1-p)*(1/n1 + 1/n2)  
> stdp<-sqrt(varp)  
> zp<-(p1 - p2)/stdp 
> zp

[1] 0

> 1-pnorm(zp)

[1] 0.5

When conducting a two-tail z-test with a 5% level of risk of a type 1 error, the critical values are -1.96 and +1.96. The z-value of 0 falls within this confidence interval, thus we fail to reject the null hypothesis that there is no difference between the proportions of patients that died with versus without cancer as part of the present problem.

Further, since the p-value of 0.5 is greater than 0.05, we, again, fail to reject the null hypothesis that the proportions of the Cancer versus non-cancer patients that died are equal.

Thus, there are equal proportions of those who died with cancer as part of the present problem and without, as well as equal proportions of those who lived with cancer as part of the present problem and without.

13.7 Vital status by Previous

H0: there is no difference between the proportion of patients that died with versus without previous admission to an ICU within 6 months, risk = 0.05
Ha: there is a difference between the proportion of patients that died with versus without previous admission to an ICU within 6 months

The following code produces a crosstab of the proportions of Previous (No and Yes) by Status (Lived or Died).

> pacman::p_load(sjPlot)
> sjt.xtab(ICU$Status, ICU$Previous, show.col.prc = TRUE)

The following code conducts a z-test and produces a z-value and a p-value for Previous.

> x1<-33; x2<-7; n1<-170; n2<-30
> p1<-x1/n1; p2<-x2/n2
> p<-(x1+x2)/(n1+n2)  
> varp<-p*(1-p)*(1/n1 + 1/n2)  
> stdp<-sqrt(varp)  
> zp<-(p1 - p2)/stdp 
> zp

[1] -0.4950738

> 1-pnorm(zp)

[1] 0.689726

When conducting a two-tail z-test with a 5% level of risk of a type 1 error, the critical values are -1.96 and +1.96. The z-value of -0.4950738 falls within this confidence interval, thus we fail to reject the null hypothesis that there is no difference between the proportion of patients that died with versus without previous admission to an ICU within 6 months of the current admission.

Further, since the p-value of 0.689726 is greater than 0.05, we, again, fail to reject the null hypothesis that there is no difference between the proportion of patients that died whether or not they were previously admitted to the ICU within the past 6 months.

Lastly, we see from the table that there was a lower percentage of patients that died with no prior ICU admission than patients that died with prior ICU admission.

13.8 Vital status by Type

H0: there is no difference between the proportion of patients that died in the elective admission group versus the emergency admission group, risk = 0.05 Ha: there is a difference between the proportion of patients that died in the elective admission group versus the emergency admission group

The following code produces a crosstab of the proportions of Type (Elective and Emergency) by Status (Lived or Died).

> pacman::p_load(sjPlot)
> sjt.xtab(ICU$Status, ICU$Type, show.col.prc = TRUE)

The following code conducts a z-test and produces a z-value and a p-value for Type.

> x1<-2; x2<-38; n1<-53; n2<-147
> p1<-x1/n1; p2<-x2/n2
> p<-(x1+x2)/(n1+n2)  
> varp<-p*(1-p)*(1/n1 + 1/n2)  
> stdp<-sqrt(varp)  
> zp<-(p1 - p2)/stdp 
> zp

[1] -3.444743

> pnorm(zp)

[1] 0.000285801

When conducting a two-tail z-test with a 5% level of risk of a type 1 error, the critical values are -1.96 and +1.96. The z-value of -3.444743 does not fall within this confidence interval, thus we reject the null hypothesis that there is no difference between the proportion of patients that died in the elective admission group versus the emergency admission group.

Further, since the p-value of 0.000285801 is less than 0.05, we, again, reject the null hypothesis that the proportions of the two groups are equal.

We can see from the table that the emergency admission type had a higher proportion of deaths than the elective admission type did.

We will now conduct a prop.test for categorical variables where the independent variable has more than 2 subgroups.

13.9 Vital status by Age

H0: there is no difference between the proportion of patients that died across the 5 age groups, risk = 0.05
Ha: the proportion of patients that died is different in at least one of the 5 age groups

We will now bin the Age variable by equal-width bins:

> ICU$Age.Binned <- with(ICU, binVariable(Age, bins=5, method='intervals', labels=c('Age group 1','Age group 2','Age group 3','Age group 4',
+   'Age group 5')))

The following code produces a crosstab of the proportions of Age (Groups 1-5) by Status (Lived or Died).

> pacman::p_load(sjPlot)
> sjt.xtab(ICU$Status, ICU$Age.Binned, show.col.prc = TRUE)

The following code conducts a z-test and produces a p-value, a chi-squared value and sample proportion estimates for Age.

> Died  <- c( 2, 2, 10, 18, 8 )
> Total <- c( 31, 19, 46, 75, 29 )
> prop.test(Died, Total)

    5-sample test for equality of proportions without continuity
    correction

data:  Died out of Total
X-squared = 6.5023, df = 4, p-value = 0.1646
alternative hypothesis: two.sided
sample estimates:
    prop 1     prop 2     prop 3     prop 4     prop 5 
0.06451613 0.10526316 0.21739130 0.24000000 0.27586207 

Since the p-value of 0.1646 is greater than 0.05, we fail to reject the null hypothesis that there is no difference between the proportion of patients that died across the 5 age groups.

Further, when conducting a chi-square test with a 5% level of risk of a type 1 error and 4 degrees of freedom, the critical value is 9.49. Since the chi-squared value of 6.5023 is less than this critical value, we, again, fail to reject the null hypothesis that there is no difference between the proportion of patients that died across the 5 age groups.

However, we can see from the sample estimates produced by the proportions test that Age group 1 and Age group 2 have slightly lower proportions than age groups 3, 4 and 5. Thus, the number of patients that died in age group 1 (the youngest age group) and age group 2 is much lower than the rest. The greatest proportion of patients that died is in group 5 (the oldest age group). Overall, proportions of death increased slightly in each age group, with closer proportions in the 3 oldest age groups and very low proportions in the 2 youngest age groups.

13.10 Vital status by Systolic Blood Pressure

H0: there is no difference between the proportion of patients that died across the 6 systolic blood pressure level groups, risk = 0.05
Ha: the proportion of patients that died is different in at least one of the 6 systolic blood pressure level groups

We grouped Systolic into medically characterized categories of hypotension, normal blood pressure, elevated blood pressure and stage 1, 2 and 3 hypertension. Hypotension is characterized by a blood pressure level of less than 80mmHg, normal blood pressure is characterized by a blood pressure level between 80 to 120mmHg, elevated blood pressure is characterized by a blood pressure level between 120 and 129mmHg, stage 1 hypertension is characterized by a blood pressure level 130-139mmHg, stage 2 hypertension is characterized by a blood pressure level 140-180mmHg, and stage 3 hypertension is characterized by a blood pressure level greater than 180mmHg.

> ICU <- 
+   within(ICU, {
+   Systolic.grouped <- Recode(Systolic, 
+   '0:80="hypotension"; 80:120="normal"; 120:129="elevated"; 130:139="stage 1 hypertension"; 140:180="stage 2 hypertension"; 180:260="stage 3 hypertension"; ;',
+    as.factor=TRUE)
+ })

The following code produces a crosstab of the proportions of Systolic (Hypotension, normal, elevated, 3 categories of hypertension) by Status (Lived or Died).

> pacman::p_load(sjPlot)
> sjt.xtab(ICU$Status, ICU$Systolic.grouped, show.col.prc = TRUE)

The following code conducts a z-test and produces a p-value, a chi-squared value and sample proportion estimates for Systolic.

> Died  <- c( 3, 9, 9, 6, 11, 2 )
> Total <- c( 17, 12, 61, 30, 65, 15 )
> prop.test(Died, Total)

    6-sample test for equality of proportions without continuity
    correction

data:  Died out of Total
X-squared = 24.597, df = 5, p-value = 0.0001667
alternative hypothesis: two.sided
sample estimates:
   prop 1    prop 2    prop 3    prop 4    prop 5    prop 6 
0.1764706 0.7500000 0.1475410 0.2000000 0.1692308 0.1333333 

Since the p-value of 0.0001667 is less than 0.05, we will reject the null hypothesis that there is no difference between the proportion of patients that died in the 6 systolic blood pressure level groups. We can see from the sample estimates that the proportions are indeed different between the 6 groups, with the highest proportion in the hypotenstion range and in the stage 1 hypertension range. The proportions in the elevated, normal, stage 2 hypertension and stage 3 hypertension groups are much lower and are quite close to each other. Thus, the hypotension and stage 1 hypertension groups had higher proportions of patients that died.

Further, when conducting a chi-square test with a 5% level of risk of a type 1 error and 5 degrees of freedom, the critical value is 11.07. Since the chi-squared value of 24.597 is greater than this critical value, we will, again, reject the null hypothesis that there is no difference between the proportion of patients that died in the 6 systolic blood pressure level groups.

13.11 Vital status by Heart Rate

H0: there is no difference between the proportion of patients that died across the bradychardia, normal heart rate and elevated heart rate groups, risk = 0.05
Ha: the proportion of patients that died is different in at least one of the 3 heart rate categories

We grouped heart rate into medically characterized categories of bradycardia, normal heart rate and tachycardia. Bradycardia is characterized by a heart rate less than 60 beats per minute, normal heart rate is characterized by a heart rate between 60-100 beats per minute, and tachycardia is characterized by a heart rate greater than 100 beats per minute.

> ICU <- 
+   within(ICU, {
+   HeartRate.grouped <- Recode(HeartRate, 
+   '0:60="bradycardia"; 60:100="normal"; 100:200="tachycardia"',
+    as.factor=TRUE)
+ })

The following code produces a crosstab of the proportions of Status (Bradycardia, Normal and Tachycardia) by Status (Lived or Died).

> pacman::p_load(sjPlot)
> sjt.xtab(ICU$Status, ICU$HeartRate.grouped, show.col.prc = TRUE)

The following code conducts a z-test and produces a p-value, a chi-squared value and sample proportion estimates for Heart Rate.

> Died  <- c( 3, 16, 21 )
> Total <- c( 15, 80, 105 )
> prop.test(Died, Total)

    3-sample test for equality of proportions without continuity
    correction

data:  Died out of Total
X-squared = 0, df = 2, p-value = 1
alternative hypothesis: two.sided
sample estimates:
prop 1 prop 2 prop 3 
   0.2    0.2    0.2 

Since the p-value of 1 is greater than 0.05, we fail to reject the null hypothesis that there is no difference between proportion of patients that died across the bradychardia, normal heart rate and elevated heart rate groups. An exact p-value of 1 means that the difference in proportions of patients that died between the 3 heart rate groups is exactly 0. Thus, there were an equal number of patients that died with bradycardia, normal heart rate and elevated heart rate.

Further, when conducting a chi-square test with a 5% level of risk of a type 1 error and 2 degrees of freedom, the critical value is 5.99. Since the chi-squared value of 0 is lower than this critical value, we, again, fail to reject the null hypothesis that there is no difference between the proportion of patients that died having bradychardia, normal heart rate and elevated heart rate.

13.12 Vital status by Consciousness

H0: there is no difference between the proportion of patients that died across the Conscious, Deep Stupor and Coma groups, risk = 0.05
Ha: the proportion of patients that died is different in at least one of the Conscious, Deep Stupor and Coma groups

The following code produces a crosstab of the proportions of Consciousness (Conscious, Deep Stupor and Coma) by Status (Lived or Died).

> pacman::p_load(sjPlot)
> sjt.xtab(ICU$Status, ICU$Consciousness, show.col.prc = TRUE)

The following code conducts a z-test and produces a p-value, a chi-squared value and sample proportion estimates for Consciousness.

> Died  <- c( 27, 5, 8 )
> Total <- c( 185, 5, 10 )
> prop.test(Died, Total)

    3-sample test for equality of proportions without continuity
    correction

data:  Died out of Total
X-squared = 45.878, df = 2, p-value = 1.091e-10
alternative hypothesis: two.sided
sample estimates:
   prop 1    prop 2    prop 3 
0.1459459 1.0000000 0.8000000 

Since the p-value of 1.091e-10 is less than 0.05, we will reject the null hypothesis that there is no difference between the proportion of patients that died across the Conscious, Deep Stupor and Coma groups.

Further, when conducting a chi-square test with a 5% level of risk of a type 1 error and 2 degrees of freedom, the critical value is 5.99. Since the chi-squared value of 45.878 is greater than this critical value, we will, again, reject the null hypothesis that there is no difference between the proportion of patients that died across the 3 Consciousness groups.

With a proportion of 1, the Deep Stupor group had the highest proportion of patients that died as all the patients with a deep stupor died. The Coma group has the second highest proportion of patients that died with a sample estimate of 80% dying. The lowest number of deaths was in the group of patients that had no coma or stupor, which is expected. Those with a deep stupor had a higher proportion of deaths than those in a coma.

From the tests of equal proportions, we note that Service (type of procedure), Type (of admission) and Conciousness had a statistically significant impact on the Vital status of patients. On the other hand, Sex, Infection, Renal, CPR, Cancer, Previous (ICU admission within the last 6 months), Age, Systolic Blood Pressure and Heart rate were not significant predictors of Vital status of patients.

14.1 Detection of outliers of Int Variables

The following variables were not significant predictors of Vital status of the patient: Cancer, Previous (ICU admission within the last 6 months), Age, Systolic Blood Pressure, Heart Rate and Race.

17.1 Logistic Regression

In order to deduce the model that will predict the outcome of the status based on our chosen variables, we had decided to conduct a logistic regression, due to the fact that our respondent variable is binomial.

According to our logistic regression model below, statistically significant indicators include age, cancer, systolic blood pressure, type, service, previous and consciousness. The large enough difference between the null and residual deviance provides us with some confidence in our model, although our confidence intervals do not as they have 0 in them. However, before we state our model based on the calculations below, we will reduce our model to its significant predictors, and further investigate whether our model is sturdy.

> ICU.m<-glm(formula=Status~Age.binned+Sex+Service+Cancer+Renal+Infection+CPR+Systolic.grouped+HeartRate.grouped+Previous+Type+PO2+Consciousness, family=binomial(logit), data=ICU)
> summary(ICU.m)

Call:
glm(formula = Status ~ Age.binned + Sex + Service + Cancer + 
    Renal + Infection + CPR + Systolic.grouped + HeartRate.grouped + 
    Previous + Type + PO2 + Consciousness, family = binomial(logit), 
    data = ICU)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.8829  -0.4709  -0.2601  -0.0640   2.4897  

Coefficients:
                                       Estimate Std. Error z value
(Intercept)                            -6.63439    2.10826  -3.147
Age.binnedGroup 2                       0.79631    0.91905   0.866
Age.binnedGroup 3                      -0.02831    0.98049  -0.029
Age.binnedGroup 4                       2.02247    0.93499   2.163
Age.binnedGroup 5                       2.59815    0.95435   2.722
SexFemale                              -0.66070    0.54423  -1.214
ServiceSurgical                        -1.07449    0.63645  -1.688
CancerYes                               3.29458    1.11696   2.950
RenalYes                                0.12988    0.75184   0.173
InfectionYes                           -0.03277    0.59850  -0.055
CPRYes                                  0.83400    0.99999   0.834
Systolic.groupedhypotension             2.48531    1.31637   1.888
Systolic.groupednormal                 -0.24664    0.90602  -0.272
Systolic.groupedstage 1 hypertension    0.17345    1.04589   0.166
Systolic.groupedstage 2 hypertension    0.06994    0.89875   0.078
Systolic.groupedstage 3 hypertension   -2.70641    1.64322  -1.647
HeartRate.groupednormal                 1.11165    1.25553   0.885
HeartRate.groupedtachycardia            0.46650    1.25586   0.371
PreviousYes                             1.54889    0.71295   2.173
TypeEmergency                           3.47421    1.29731   2.678
PO2Yes                                 -1.12282    1.00804  -1.114
ConsciousnessDeep Stupor               22.15464 1493.02278   0.015
ConsciousnessComa                       3.40765    1.34549   2.533
                                     Pr(>|z|)   
(Intercept)                           0.00165 **
Age.binnedGroup 2                     0.38625   
Age.binnedGroup 3                     0.97696   
Age.binnedGroup 4                     0.03053 * 
Age.binnedGroup 5                     0.00648 **
SexFemale                             0.22475   
ServiceSurgical                       0.09136 . 
CancerYes                             0.00318 **
RenalYes                              0.86285   
InfectionYes                          0.95634   
CPRYes                                0.40428   
Systolic.groupedhypotension           0.05903 . 
Systolic.groupednormal                0.78545   
Systolic.groupedstage 1 hypertension  0.86828   
Systolic.groupedstage 2 hypertension  0.93797   
Systolic.groupedstage 3 hypertension  0.09956 . 
HeartRate.groupednormal               0.37594   
HeartRate.groupedtachycardia          0.71030   
PreviousYes                           0.02982 * 
TypeEmergency                         0.00741 **
PO2Yes                                0.26534   
ConsciousnessDeep Stupor              0.98816   
ConsciousnessComa                     0.01132 * 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 200.16  on 199  degrees of freedom
Residual deviance: 113.90  on 177  degrees of freedom
AIC: 159.9

Number of Fisher Scoring iterations: 16

> confint(ICU.m)

                                            2.5 %     97.5 %
(Intercept)                           -11.2943293 -2.9183994
Age.binnedGroup 2                      -0.9845178  2.7306204
Age.binnedGroup 3                      -1.9841072  1.9925381
Age.binnedGroup 4                       0.2829682  4.0461747
Age.binnedGroup 5                       0.8427448  4.6641819
SexFemale                              -1.7796928  0.3753063
ServiceSurgical                        -2.3924683  0.1322101
CancerYes                               1.2162772  5.7378792
RenalYes                               -1.4328515  1.5686034
InfectionYes                           -1.2264859  1.1514648
CPRYes                                 -1.2229901  2.7790263
Systolic.groupedhypotension             0.0492908  5.2865460
Systolic.groupednormal                 -1.9894751  1.6416260
Systolic.groupedstage 1 hypertension   -1.8759776  2.3029733
Systolic.groupedstage 2 hypertension   -1.6435452  1.9585803
Systolic.groupedstage 3 hypertension   -6.4558896  0.2342551
HeartRate.groupednormal                -1.0472842  4.0750579
HeartRate.groupedtachycardia           -1.7630972  3.3596867
PreviousYes                             0.1451916  2.9812219
TypeEmergency                           1.3260542  6.7287588
PO2Yes                                 -3.3410665  0.7062389
ConsciousnessDeep Stupor             -131.5510230         NA
ConsciousnessComa                       0.9466277  6.3280206

> exp(coef(ICU.m))

                         (Intercept)                    Age.binnedGroup 2 
                        1.314382e-03                         2.217333e+00 
                   Age.binnedGroup 3                    Age.binnedGroup 4 
                        9.720847e-01                         7.557003e+00 
                   Age.binnedGroup 5                            SexFemale 
                        1.343889e+01                         5.164922e-01 
                     ServiceSurgical                            CancerYes 
                        3.414735e-01                         2.696616e+01 
                            RenalYes                         InfectionYes 
                        1.138693e+00                         9.677654e-01 
                              CPRYes          Systolic.groupedhypotension 
                        2.302504e+00                         1.200485e+01 
              Systolic.groupednormal Systolic.groupedstage 1 hypertension 
                        7.814207e-01                         1.189401e+00 
Systolic.groupedstage 2 hypertension Systolic.groupedstage 3 hypertension 
                        1.072445e+00                         6.677639e-02 
             HeartRate.groupednormal         HeartRate.groupedtachycardia 
                        3.039363e+00                         1.594400e+00 
                         PreviousYes                        TypeEmergency 
                        4.706237e+00                         3.227245e+01 
                              PO2Yes             ConsciousnessDeep Stupor 
                        3.253609e-01                         4.184463e+09 
                   ConsciousnessComa 
                        3.019420e+01 

> ICU.final.m<-glm(formula=Status~Age.binned+Service+Cancer+Systolic.grouped+Consciousness+Previous+Type, family=binomial(logit),data=ICU)
> summary(ICU.final.m)

Call:
glm(formula = Status ~ Age.binned + Service + Cancer + Systolic.grouped + 
    Consciousness + Previous + Type, family = binomial(logit), 
    data = ICU)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-2.30437  -0.51110  -0.28167  -0.07613   2.54830  

Coefficients:
                                       Estimate Std. Error z value
(Intercept)                            -5.99744    1.71089  -3.505
Age.binnedGroup 2                       0.74928    0.86787   0.863
Age.binnedGroup 3                       0.02170    0.94389   0.023
Age.binnedGroup 4                       1.42785    0.84632   1.687
Age.binnedGroup 5                       2.28294    0.86739   2.632
ServiceSurgical                        -0.91971    0.55234  -1.665
CancerYes                               3.22412    1.06372   3.031
Systolic.groupedhypotension             1.88610    1.16403   1.620
Systolic.groupednormal                 -0.21794    0.85482  -0.255
Systolic.groupedstage 1 hypertension    0.09025    0.96050   0.094
Systolic.groupedstage 2 hypertension    0.23025    0.84390   0.273
Systolic.groupedstage 3 hypertension   -2.60303    1.51526  -1.718
ConsciousnessDeep Stupor               21.44683 1572.96411   0.014
ConsciousnessComa                       3.19219    1.03515   3.084
PreviousYes                             1.32364    0.66415   1.993
TypeEmergency                           3.47964    1.29137   2.695
                                     Pr(>|z|)    
(Intercept)                          0.000456 ***
Age.binnedGroup 2                    0.387942    
Age.binnedGroup 3                    0.981661    
Age.binnedGroup 4                    0.091579 .  
Age.binnedGroup 5                    0.008489 ** 
ServiceSurgical                      0.095888 .  
CancerYes                            0.002438 ** 
Systolic.groupedhypotension          0.105164    
Systolic.groupednormal               0.798761    
Systolic.groupedstage 1 hypertension 0.925137    
Systolic.groupedstage 2 hypertension 0.784972    
Systolic.groupedstage 3 hypertension 0.085819 .  
ConsciousnessDeep Stupor             0.989121    
ConsciousnessComa                    0.002044 ** 
PreviousYes                          0.046265 *  
TypeEmergency                        0.007049 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 200.16  on 199  degrees of freedom
Residual deviance: 119.76  on 184  degrees of freedom
AIC: 151.76

Number of Fisher Scoring iterations: 16

> confint(ICU.final.m)

                                             2.5 %     97.5 %
(Intercept)                          -9.872787e+00 -2.9758853
Age.binnedGroup 2                    -9.269851e-01  2.5835764
Age.binnedGroup 3                    -1.852435e+00  1.9673144
Age.binnedGroup 4                    -1.597920e-01  3.2532500
Age.binnedGroup 5                     6.943378e-01  4.1819402
ServiceSurgical                      -2.062763e+00  0.1239095
CancerYes                             1.241663e+00  5.5829700
Systolic.groupedhypotension          -2.975703e-01  4.3473638
Systolic.groupednormal               -1.850946e+00  1.5794947
Systolic.groupedstage 1 hypertension -1.803025e+00  2.0529066
Systolic.groupedstage 2 hypertension -1.364411e+00  2.0213164
Systolic.groupedstage 3 hypertension -6.109662e+00  0.1221235
ConsciousnessDeep Stupor             -1.409386e+02         NA
ConsciousnessComa                     1.316358e+00  5.5297057
PreviousYes                           1.278671e-04  2.6418700
TypeEmergency                         1.362320e+00  6.7326806

> exp(coef(ICU.final.m))

                         (Intercept)                    Age.binnedGroup 2 
                        2.485115e-03                         2.115474e+00 
                   Age.binnedGroup 3                    Age.binnedGroup 4 
                        1.021934e+00                         4.169717e+00 
                   Age.binnedGroup 5                      ServiceSurgical 
                        9.805506e+00                         3.986338e-01 
                           CancerYes          Systolic.groupedhypotension 
                        2.513138e+01                         6.593579e+00 
              Systolic.groupednormal Systolic.groupedstage 1 hypertension 
                        8.041750e-01                         1.094451e+00 
Systolic.groupedstage 2 hypertension Systolic.groupedstage 3 hypertension 
                        1.258920e+00                         7.404889e-02 
            ConsciousnessDeep Stupor                    ConsciousnessComa 
                        2.061761e+09                         2.434157e+01 
                         PreviousYes                        TypeEmergency 
                        3.757058e+00                         3.244790e+01 

> pacman::p_load(rsample,DT)
> set.seed(78)
> train_test_split <- initial_split(ICU)
> train <- training(train_test_split)
> test <- testing(train_test_split)
> (samp <- dim(train_test_split))

  analysis assessment          n          p 
       150         50        200         25 

> datatable(train)

> ICU.tr<-glm(Status~Age.binned+Service+Cancer+Systolic.grouped+Previous+Consciousness+Type, family=binomial(logit),data=train)
> summary(ICU.tr)

Call:
glm(formula = Status ~ Age.binned + Service + Cancer + Systolic.grouped + 
    Previous + Consciousness + Type, family = binomial(logit), 
    data = train)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-2.23081  -0.45015  -0.07818  -0.00002   2.43434  

Coefficients:
                                      Estimate Std. Error z value Pr(>|z|)
(Intercept)                           -40.1228  4921.3736  -0.008   0.9935
Age.binnedGroup 2                       0.2123     1.0653   0.199   0.8420
Age.binnedGroup 3                       0.3680     1.0733   0.343   0.7317
Age.binnedGroup 4                       0.3774     1.0534   0.358   0.7201
Age.binnedGroup 5                       1.5838     1.0429   1.519   0.1288
ServiceSurgical                        -1.2139     0.7177  -1.691   0.0908
CancerYes                               4.0976     1.6469   2.488   0.0128
Systolic.groupedhypotension            20.3716  4350.2391   0.005   0.9963
Systolic.groupednormal                 17.8232  4350.2390   0.004   0.9967
Systolic.groupedstage 1 hypertension   18.5208  4350.2390   0.004   0.9966
Systolic.groupedstage 2 hypertension   18.6956  4350.2390   0.004   0.9966
Systolic.groupedstage 3 hypertension   15.7793  4350.2393   0.004   0.9971
PreviousYes                             1.0038     0.8410   1.194   0.2327
ConsciousnessDeep Stupor               40.7402  6647.7825   0.006   0.9951
ConsciousnessComa                       3.9932     1.5764   2.533   0.0113
TypeEmergency                          19.7312  2301.1604   0.009   0.9932
                                      
(Intercept)                           
Age.binnedGroup 2                     
Age.binnedGroup 3                     
Age.binnedGroup 4                     
Age.binnedGroup 5                     
ServiceSurgical                      .
CancerYes                            *
Systolic.groupedhypotension           
Systolic.groupednormal                
Systolic.groupedstage 1 hypertension  
Systolic.groupedstage 2 hypertension  
Systolic.groupedstage 3 hypertension  
PreviousYes                           
ConsciousnessDeep Stupor              
ConsciousnessComa                    *
TypeEmergency                         
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 144.406  on 149  degrees of freedom
Residual deviance:  70.376  on 134  degrees of freedom
AIC: 102.38

Number of Fisher Scoring iterations: 19

> exp(coef(ICU.tr))

                         (Intercept)                    Age.binnedGroup 2 
                        3.757317e-18                         1.236558e+00 
                   Age.binnedGroup 3                    Age.binnedGroup 4 
                        1.444786e+00                         1.458544e+00 
                   Age.binnedGroup 5                      ServiceSurgical 
                        4.873390e+00                         2.970322e-01 
                           CancerYes          Systolic.groupedhypotension 
                        6.019612e+01                         7.035111e+08 
              Systolic.groupednormal Systolic.groupedstage 1 hypertension 
                        5.501992e+07                         1.105283e+08 
Systolic.groupedstage 2 hypertension Systolic.groupedstage 3 hypertension 
                        1.316382e+08                         7.125962e+06 
                         PreviousYes             ConsciousnessDeep Stupor 
                        2.728531e+00                         4.934409e+17 
                   ConsciousnessComa                        TypeEmergency 
                        5.422580e+01                         3.708115e+08 

17.2 Testing & training the model

As we can see below, where we have used the training model to predict the models in the testing dataset, we do get mixed results regarding the statistical significance of the predictors based on the CIs. For example, all predictors are positive as we can see above, yet only age binned group 5, cancer,consciousness coma, previous, and type have their lower CIs above 1. Intercept does not have a lower coefficient above 1, nor does systolic thus further cementing the fact that it is not statistically significant.

> predicted.val<-predict(ICU.tr, newdata=test)
> head(predicted.val)

         2          7          8         11         15         17 
 -1.196692 -23.145574  -1.696054 -24.341391  -4.244406 -22.428841 

> predicted.prob <- predict(ICU.tr, test, type = "response")
> head( predict( ICU.tr, test, type="response") )

           2            7            8           11           15 
2.320642e-01 8.871659e-11 1.549813e-01 2.683295e-11 1.414141e-02 
          17 
1.816679e-10 

> predicted.classes <- ifelse( predicted.prob > 0.5, "Lived", "Dead" )
> head(predicted.classes)

     2      7      8     11     15     17 
"Dead" "Dead" "Dead" "Dead" "Dead" "Dead" 

> tab_model(
+   ICU.tr,
+   title = "Logistic Regression Odds Ratios for Status using the Training Sample",
+   show.stat = TRUE,
+   digits = 3,
+   string.stat = "z-value",
+   string.p = "p (sig)",
+   show.fstat = TRUE,
+   show.dev = TRUE,
+   show.aic = TRUE,
+   CSS = list(
+     css.depvarhead = 'color: red;',
+     css.centeralign = 'text-align: left;',
+     css.firsttablecol = 'font-weight: bold;',
+     css.summary = 'color: blue;'
+   )
+ )

> plot_model(
+   ICU.tr,
+   title = "Logistic Regression of State of Status using the Training Sample",
+   show.p = TRUE
+ )  + ylim(0, 800)

With regards to the multicollinearity present within the model, according to the VIFs below, none are equal to 4, thus demonstrating the lack of multicollinarity in this model.

> pacman::p_load(car,corrplot)
> vf<-vif(ICU.tr)
> vf

                     GVIF Df GVIF^(1/(2*Df))
Age.binned       1.928971  4        1.085590
Service          1.182827  1        1.087579
Cancer           1.463451  1        1.209732
Systolic.grouped 2.173679  5        1.080736
Previous         1.310050  1        1.144574
Consciousness    1.637686  2        1.131248
Type             1.136135  1        1.065897

Although we have deduced that there is no multicollinearity present, we will now test the model against the null model, based on the training data. Below, we see that it’s intercept is still significant.

> fit0<-glm(Status~1, family=binomial(logit), data=train)
> summary(fit0)

Call:
glm(formula = Status ~ 1, family = binomial(logit), data = train)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-0.6428  -0.6428  -0.6428  -0.6428   1.8322  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)  -1.4718     0.2095  -7.024 2.16e-12 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 144.41  on 149  degrees of freedom
Residual deviance: 144.41  on 149  degrees of freedom
AIC: 146.41

Number of Fisher Scoring iterations: 4

Below, however, we attempt to fit all of the predictors, using the training data. We still see that the all of the predictors are statistically significant, thus demonstrating that this model is worth pursuing. This is further confirmed by the ANOVA chi-square conducted below, which is also statistically significant.

> fitall<-glm(Status~Age.binned+Service+Cancer+Systolic.grouped+Previous+Consciousness+Type, family=binomial(logit), data=train)
> summary(fitall)

Call:
glm(formula = Status ~ Age.binned + Service + Cancer + Systolic.grouped + 
    Previous + Consciousness + Type, family = binomial(logit), 
    data = train)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-2.23081  -0.45015  -0.07818  -0.00002   2.43434  

Coefficients:
                                      Estimate Std. Error z value Pr(>|z|)
(Intercept)                           -40.1228  4921.3736  -0.008   0.9935
Age.binnedGroup 2                       0.2123     1.0653   0.199   0.8420
Age.binnedGroup 3                       0.3680     1.0733   0.343   0.7317
Age.binnedGroup 4                       0.3774     1.0534   0.358   0.7201
Age.binnedGroup 5                       1.5838     1.0429   1.519   0.1288
ServiceSurgical                        -1.2139     0.7177  -1.691   0.0908
CancerYes                               4.0976     1.6469   2.488   0.0128
Systolic.groupedhypotension            20.3716  4350.2391   0.005   0.9963
Systolic.groupednormal                 17.8232  4350.2390   0.004   0.9967
Systolic.groupedstage 1 hypertension   18.5208  4350.2390   0.004   0.9966
Systolic.groupedstage 2 hypertension   18.6956  4350.2390   0.004   0.9966
Systolic.groupedstage 3 hypertension   15.7793  4350.2393   0.004   0.9971
PreviousYes                             1.0038     0.8410   1.194   0.2327
ConsciousnessDeep Stupor               40.7402  6647.7825   0.006   0.9951
ConsciousnessComa                       3.9932     1.5764   2.533   0.0113
TypeEmergency                          19.7312  2301.1604   0.009   0.9932
                                      
(Intercept)                           
Age.binnedGroup 2                     
Age.binnedGroup 3                     
Age.binnedGroup 4                     
Age.binnedGroup 5                     
ServiceSurgical                      .
CancerYes                            *
Systolic.groupedhypotension           
Systolic.groupednormal                
Systolic.groupedstage 1 hypertension  
Systolic.groupedstage 2 hypertension  
Systolic.groupedstage 3 hypertension  
PreviousYes                           
ConsciousnessDeep Stupor              
ConsciousnessComa                    *
TypeEmergency                         
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 144.406  on 149  degrees of freedom
Residual deviance:  70.376  on 134  degrees of freedom
AIC: 102.38

Number of Fisher Scoring iterations: 19

> anova(fitall, fit0, test="Chisq")

Analysis of Deviance Table

Model 1: Status ~ Age.binned + Service + Cancer + Systolic.grouped + Previous + 
    Consciousness + Type
Model 2: Status ~ 1
  Resid. Df Resid. Dev  Df Deviance Pr(>Chi)    
1       134     70.376                          
2       149    144.406 -15   -74.03 8.47e-10 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

We have also conducted a Wald test to test the significance of the predictors in the training model as well. According to the results, cancer, type,consciousness, and previous are statistically significant.

> pacman::p_load(survey)
> regTermTest(ICU.tr, "Age.binned")

Wald test for Age.binned
 in glm(formula = Status ~ Age.binned + Service + Cancer + Systolic.grouped + 
    Previous + Consciousness + Type, family = binomial(logit), 
    data = train)
F =  0.714926  on  4  and  134  df: p= 0.58313 

> regTermTest(ICU.tr, "Cancer")

Wald test for Cancer
 in glm(formula = Status ~ Age.binned + Service + Cancer + Systolic.grouped + 
    Previous + Consciousness + Type, family = binomial(logit), 
    data = train)
F =  6.190383  on  1  and  134  df: p= 0.014071 

> regTermTest(ICU.tr, "Systolic.grouped")

Wald test for Systolic.grouped
 in glm(formula = Status ~ Age.binned + Service + Cancer + Systolic.grouped + 
    Previous + Consciousness + Type, family = binomial(logit), 
    data = train)
F =  1.456501  on  5  and  134  df: p= 0.20829 

> regTermTest(ICU.tr, "Type")

Wald test for Type
 in glm(formula = Status ~ Age.binned + Service + Cancer + Systolic.grouped + 
    Previous + Consciousness + Type, family = binomial(logit), 
    data = train)
F =  7.352134e-05  on  1  and  134  df: p= 0.99317 

> regTermTest(ICU.tr, "Service")

Wald test for Service
 in glm(formula = Status ~ Age.binned + Service + Cancer + Systolic.grouped + 
    Previous + Consciousness + Type, family = binomial(logit), 
    data = train)
F =  2.860549  on  1  and  134  df: p= 0.093101 

> regTermTest(ICU.tr, "Consciousness")

Wald test for Consciousness
 in glm(formula = Status ~ Age.binned + Service + Cancer + Systolic.grouped + 
    Previous + Consciousness + Type, family = binomial(logit), 
    data = train)
F =  3.208147  on  2  and  134  df: p= 0.043556 

> regTermTest(ICU.tr, "Previous")

Wald test for Previous
 in glm(formula = Status ~ Age.binned + Service + Cancer + Systolic.grouped + 
    Previous + Consciousness + Type, family = binomial(logit), 
    data = train)
F =  1.424478  on  1  and  134  df: p= 0.23478 

Now that we have deduced that our model is indeed robust, we will now move on to deduce our classificantion and regression trees, based on our variables of interest.

17.3 Classification and Regression Trees

As we can see below, the variables of interest are age, systolic, service and type. Pruning the tree doesn’t seem plausible, as the xerror is steady from lines 2 to 4 and our cp graph denotes a stable cp from size 3 to 7, while the mean acuracy for our regression tree is 0.88.

> pacman::p_load(rpart, rpart.plot, rattle, dplyr)
> set.seed(2715)
> 
> icutree=rpart(Status~Age.binned+Cancer+Systolic.grouped+Type+Consciousness+Type+Service+Renal+Infection+CPR+HeartRate.grouped+Previous+Consciousness, method="class", data=ICU)
> fancyRpartPlot(icutree)

> printcp(icutree)

Classification tree:
rpart(formula = Status ~ Age.binned + Cancer + Systolic.grouped + 
    Type + Consciousness + Type + Service + Renal + Infection + 
    CPR + HeartRate.grouped + Previous + Consciousness, data = ICU, 
    method = "class")

Variables actually used in tree construction:
[1] Age.binned       Consciousness    Service          Systolic.grouped
[5] Type            

Root node error: 40/200 = 0.2

n= 200 

      CP nsplit rel error xerror    xstd
1 0.2750      0     1.000  1.000 0.14142
2 0.0750      1     0.725  0.725 0.12449
3 0.0125      2     0.650  0.775 0.12795
4 0.0100      6     0.600  0.825 0.13123

> predicted.classes <- icutree %>% predict(, data=icu, type = "class")
> head(predicted.classes, 12)

    1     2     3     4     5     6     7     8     9    10    11    12 
Lived Lived Lived Lived Lived Lived Lived Lived Lived Lived Lived Lived 
Levels: Lived Died

> mean(predicted.classes == ICU$Status)

[1] 0.88

> plotcp(icutree)

> par(mfrow=c(1,2)) 
> rsq.rpart(icutree)

Classification tree:
rpart(formula = Status ~ Age.binned + Cancer + Systolic.grouped + 
    Type + Consciousness + Type + Service + Renal + Infection + 
    CPR + HeartRate.grouped + Previous + Consciousness, data = ICU, 
    method = "class")

Variables actually used in tree construction:
[1] Age.binned       Consciousness    Service          Systolic.grouped
[5] Type            

Root node error: 40/200 = 0.2

n= 200 

      CP nsplit rel error xerror    xstd
1 0.2750      0     1.000  1.000 0.14142
2 0.0750      1     0.725  0.725 0.12449
3 0.0125      2     0.650  0.775 0.12795
4 0.0100      6     0.600  0.825 0.13123

> icutree.train=rpart(Status~Service+Cancer+Previous+Type+Age.binned+Systolic.grouped+HeartRate.grouped+Consciousness+CPR+Infection+Sex+Renal, method="class", data=train, minsplit=20)
> fancyRpartPlot(icutree.train)

> plotcp(icutree.train)

> par(mfrow=c(1,2)) 
> rsq.rpart(icutree.train) 

Classification tree:
rpart(formula = Status ~ Service + Cancer + Previous + Type + 
    Age.binned + Systolic.grouped + HeartRate.grouped + Consciousness + 
    CPR + Infection + Sex + Renal, data = train, method = "class", 
    minsplit = 20)

Variables actually used in tree construction:
[1] Consciousness

Root node error: 28/150 = 0.18667

n= 150 

       CP nsplit rel error  xerror    xstd
1 0.35714      0   1.00000 1.00000 0.17043
2 0.01000      1   0.64286 0.64286 0.14214

> trainfit<-prune(icutree.train,cp=icutree.train$cptable[which.min(icutree.train$cptable[,"xerror"]),"CP"])
> fancyRpartPlot(trainfit, palettes = "YlOrRd" , caption=NULL  )

> tree.pred.train.full=predict(icutree.train, newdata=train, type="class")
> 
> table_mat_full<-table(train$Status, tree.pred.train.full)
> 
> sjt.xtab(train$Status, tree.pred.train.full, var.labels=c("Actual Status", "Predicted Status"), show.row.prc = TRUE)

> (accuracy_Train_Test <- sum(diag(table_mat_full)) / sum(table_mat_full))

[1] 0.88

> tree.pred.test.full = predict(icutree.train, newdata=test, type = "class")
> table_mat_tr_full <- table(test$Status, tree.pred.test.full)
> sjt.xtab(test$Status, tree.pred.test.full, var.labels = c("Actual Status", "Predicted Status"), show.row.prc = TRUE)

> (accuracy_Train_Test_full <- sum(diag(table_mat_tr_full)) / sum(table_mat_tr_full))

[1] 0.78

> rpart.rules(trainfit)

 Status                                          
   0.12 when Consciousness is           Conscious
   0.92 when Consciousness is Deep Stupor or Coma